1) The crystals are most likely deposits left from the evaporation of water that used to be in the tank (as you mentioned, you had the lid off). As the water evaporated, the dissolved minerals transitioned into their natural crystalline structure, which is attractive to the dissolved minerals -- rinse and repeat and you have a larger crystal structure adhered to the wall.
2) You could -- but from the look, my personal preference would be to empty it and give it a good and thorough cleaning.
3) A thorough cleaning once a year is often recommended. Is it necessary? Maybe not, but it couldn't hurt anything either. I'm sure your owner's manual outlines a deep cleaning procedure, but if not, there are a number of resources on the internet.
Regarding the disinfection -- I would follow the manufacturers recommendations. You should use a fragrence-free bleach. Store-brand bleaches often have less additives than Clorox, which is good when the use is "food"-related. Clorox uses additives which aid in the removal of soils (things like caustic soda, soda ash), surfactants, and other ingredients to help prevent stains (sodium polyacrylate). 4 oz does seem a bit much, but the manufacturer would know better than me what should be used.
4) I'm not sure why your manual does not recommend the mixture of potassium chloride and sodium chloride -- these are mixed in water softeners quite often to decrease the saltiness of the drinking water and save a bit of money. My vote is, when in doubt, follow the manufacturers recommendations -- they only spent millions developing the thing (of course, they would also like to make money when you need to replace it, so it's a bit of a double-edged sword).
It sounds like it's an activated carbon filter, which takes organics out of the water (like the sulphur smell), and that it needs to be rebedded (this needs to happen typically once every 3 to 5 years, depending on level of contamination). Once the activated carbon is 'used up', it actually becomes a good breeding ground for bacteria and is worse than completely ineffective. (Aside, this is the same reason that jug-style filters like Britta need to be replaced regularly -- and it's better to use nothing than an old one).
![activated carbon pores](https://i.stack.imgur.com/MSB0P.jpg)
There is not really anything called an "iron filter". Softeners can low levels of iron out, and greensand filters can be used for higher levels, but a greensand filter will have a small tank attached with potassium permanganate (dark purple stuff) in it:
![Potassium permanganate tank attached to greensand filter](https://i.stack.imgur.com/z2iPN.jpg)
Best Answer
Usually a brown color discoloration in a water system, such as a softener unit, is due to iron. Iron combines with oxygen to form iron oxide which is reddish brown in color.
You may be more familiar with rust on metal parts made of iron. Rust is simply iron oxide.